The problem is that virtually everything is now on spot beams. The E10 minneapolis spot doesn't even come close to making it down to St Louis. You can "move", but you will probably not get signal for SD locals.
The Minneapolis HD is currently on 129, which is a national beam. This would get you the 4 networks. I don't know which local covers the major sports, but it is probably not one of the 4 big stations. The HD locals have been recently uplinked on 61.5 spotbeam, so this could change in the future.
The SD RSNs are still mostly on nat beams, but the HD ones have been going spot recently.